Compact planar microstripline branch-line and rat-race couplers

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A novel approach to the design and implementation of dual-band compact planar 90/spl deg/ branch-line coupler (2004, background): “Over the past years, various reports concerning bandwidth enhancement [3] and size reduction [4]–[6] techniques have been published in the literature.”
Compact Planar Microstrip Branch-Line Couplers Using the Quasi-Lumped Elements Approach With Nonsymmetrical and Symmetrical T-Shaped Structure (2006, background): “The conventional distributed capacitive loading is the open-end stub line [17], [22], [23].”
Miniaturized fractal rat-race, branch-line, and coupled-line hybrids (2004, neutral): “Numerous methods have been developed to reduce the size of these topologies [2]–[5].”
A Compact Slow-Wave Microstrip Branch-Line Coupler With High Performance (2007, methodology): “In [4], a microstrip branch-line coupler was designed by periodically loading open end stubs with the coupler, however, the saved size of this coupler is only 37% compared to the standard design.”